This discussion strikes me as treating marriage fairly strangely. It's a legal category of relationship. It's another form of a de facto relationship (the name 'de facto' is a product of history more than anything else; it's not implying that the relationship is not a legal one). A de facto relationship isn't something you register for. If your relationship has characteristics A, B and C, the government will treat you as being in a de facto relationship. It's not really a matter of choice, other than the choice involved in being in a relationship with those characteristics. A 'marriage' is just the government recognising that you've also had some sort of ceremony which indicates an intention for a greater degree of permanence. Should a de facto relationship cease to have characteristics A, B and C, it will cease to be a de facto relationship. It seems odd to suggest that, should a marriage also cease to have characteristics A, B and C, the government should insist on continuing to recognise it as a marriage, where it doesn't do the same for de facto relationships. It would no longer fit the purposes for which the legal category exists. If 'marriage' is descriptive of the relationship, if the nature of that relationship changes, it simply doesn't make sense to continue applying the same term to it.
Unless you're actually saying that the government should force individuals to live together and share property, insisting on regarding couples as 'married', even when they have separated, or no longer have any meaningful relationship to speak of, just means that the property will not be distributed according to the actual nature of the relationship. Divorce is essentially just signifying that this distribution should take place, as it does with de facto relationships. This state of affairs is quite inefficient, and historically unfair to women.
I'm highly sceptical as to the arguments in the OP. The supposed detriments do not strike me as necessary results of no-fault divorce. Rather, they're probably description of how no-fault divorce has operated within a given system of law. With child custody, for instance, there's no reason why no-fault divorce would necessarily grant women greater custody rights over children; that's simply a quirk of the system in which no-fault divorce is being observed.